Let f(x) be a cubic polynomial function such that y=13(x-1)+4 is tangent to the graph of f(x)at (1, 4) and y=(x+1)+6 is tangent to the graph of f(x) at (-1, 6). Find the equation of f(x)

31,136 results
  1. math

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=7x-5x^2 at (-2,-34) m = ?? y = ?? .

  2. Math

    Which of the following statements about a polynomial function is false? 1) A polynomial function of degree n has at most n turning points. 2) A polynomial function of degree n may have up to n distinct zeros. 3) A polynomial function of odd degree may have

  3. pre-calc

    1. which of the following is a fourth degree polynomial function? select all that apply. a. f(x)= 4x^3 - x^2 + 2x - 7 b. f(x)= 5-x^4 c. f(x)= 1 / 2x^4 + x^2 -5 d. f(x)= 3x^4 + 2x^3 -4x +1 2. which function below has the end behavior f(x) approaches neg.

  4. algebra

    Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. 2 – 11x^2 – 8x + 6x^2 A. –5x^2 – 8x + 2; quadratic trinomial B. –5x^2 – 8x; quadratic binomial C. –6x^2 – 8x – 2; cubic polynomial D.

  5. calculus

    Let f be a differentiable function such that f(4)=7 and f′(4)=15. The graph of f is concave up on the interval (3,5). Which of the following is true about the approximation for f(3.5) found using the line tangent to the graph of f at x=4 ?

  6. Calculus

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 7 x - 2 x^2 text( at ) \(-1,-9\) m = y =

  7. Calculus - Functions?

    #1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of a and b #2. Let h be a

  8. calculus

    If a function f is continuous for all x and if f has a relative minimum at (-1,4) and a relative minimum at (-3,2), which of the following statements must be true? (a) The graph of f has a point of inflection somewhere between x = -1 and x=3 (b) f'(-1) = 0

  9. Calculus

    Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. a.Find all values of x where the graph of g has a critical value. b.For each critical value, state whether the

  10. CALCULUS HELP

    Write the equation of the tangent line to the graph of the function at the indicated point. Check the reasonableness of your answer by graphing both the function and the tangent line. Y=(x-2)/(15-x^2) x=-4 HOW DO WE DO THIS

  11. Calculus

    1. On what interval is the function f(x)=x^3-4x^2+5x concave upward? 2. For what values of x dies the graph of f(x)=2x^3-3x^2-6x+87 have a horizontal tangent? Is there no solution because the equation can't be factored? 3. At what point on the curve

  12. Calc.

    Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the x-axis. I don't really get what this question is asking. It looks like the area of right triangle to me...try the graph, and shade the area under

  13. Calculus

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at x=-1 and x=3 and has a

  14. Algebra

    Below is the graph of a polynomial function f with real coefficients. Use the graph to answer the following questions about f. All local extrema of f are shown in the graph. I really need help with this one but I can't post the graph.

  15. Calculus

    1. a) For the Function and point below , Find f’(a). b) Determine the equation of the line tangent to the graph of f at (a,f(a)) for the given value of f(x) = 4x2+2x, a =1 F’(a) = y = 2. For the function find f’ using the definition f’(x) =

  16. calculus

    find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8

  17. Calc

    Write the equation of the line tangent to the graph of the function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct. (1/x^3 -x)^2 at x= 2

  18. Calculus (Continuity and Differentiability)

    Okay. So I am given a graph of a derivative. From what I can gather, it looks like the function might be abs(x-2)-4. (I was not given an explicit function for g', just its graph.) The question then goes on to ask me: Is it possible, impossible, or certain

  19. Calc

    Consider the cubic polynomial y=Ax^3 +6x^2 -Bx, where A and B are unknown constants. If possible determine the values of A and B so that the graph of y has a maximum value at x=-1 and an inflection point at 1.

  20. math

    Using only​ algebra, find a cubic function with the given zeros. -2, 3, -7 the polynomial function is: f(x)=x^3+ (BLANK) x^2-13x-42 i can't figure out what BLANK is Thank you!

  21. algebra

    file:///C:/Users/Pat/Downloads/IMG_0166.JPG Above is a graph of a polynomial function ƒ with real coefficients. Use graph to answer following questions about ƒ. All local extreme of ƒ are shown on graph. a. the function is decreasing over which

  22. Math

    What does the degree of a polynomial expression tell you about its related polynomial function? Explain your thinking. Give an example of a polynomial expression of degree three. Provide information regarding the graph and zeros of the related polynomial

  23. calculus

    let f be the function f(x) = x^3 + 3x^2 - x + 2 a. the tangent to the graph of f at the point P = (-2,8) intersects the graph of f again at the point Q. Find the coordinates of point Q. b. Find the coordinates of point R, the inflection point of the graph

  24. Calculus

    1. a) For the Function and point below , Find f’(a). b) Determine the equation of the line tangent to the graph of f at (a,f(a)) for the given value of f(x) = 4x2+2x, a =1 F’(a) = y = 2. For the function find f’ using the definition f’(x) =

  25. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4. Find all values of x on the

  26. Calculus

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/4 x at (1,15/4)

  27. Calculus

    Suppose that ax^2 + bx + c is a quadratic polynomial and that the integration: Int 1/(ax^2 + bx + c) dx produces a function with neither a logarithmic or inverse tangent term. What does this tell you about the roots of the polynomial?

  28. Calculus

    A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and the graph of f has a point

  29. calculus

    Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. Find all values of x where the graph of g has a critical value. For each critical value, state whether the graph

  30. calculus

    Let f be the function given by f(x)= x^2+4x-8. The tangent line to the graph at x=2 is used to approximate values of f. For what value(s) of x is the tangent line approximation twice that of f?

  31. Math Help TIMED!

    write the polynomial in standard form then name the polynomial based on its degree and number of terms 10 g - 7 g^3 + 2g^2 - 5 a. -7g^3 + 2g^2 + 10g - 5 cubic polynomial b. -5 + 10g + 2g^2 - 7g^3 cubic binomial c. 7g^3 - 2g^2 + 10g - 5 quadratic binomial

  32. Algebra 2

    Describe the end behavior of the graph of the polynomial function. Then evaluate the function for x=-4, -3, -2, -1, 0, 1, 2, 3, 4. Then graph the function.y=x^4-2x^2-x-1 and y=(x-3)(x+1)(x+2)

  33. math

    weloo. Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation of the line normal to the graph of f(x) when x= pie/6 . (b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal. (c)Find the absolute

  34. cal

    Equations of the tangent lines to hyperbola xy=1 that pass through point (-1,1) I know the graph of y=1/x but not sure about the tangent lines at given point. Are the lines tangent to (1,1) and (-1,-1)? You're correct, the graph is y=1/x, so find y' to get

  35. 8th grade algebra

    A gardner at a nursery is filling pots with soil to prepare to transplant seedlings into these larger pots. Each new pot needs about 27 cubic inches of soil. The amount of soil s (in cubic inches) it takes to fill p pots is given by the function s=27p. a.

  36. Algebra 1

    A gardener at a nursery is filling pots with soil to prepare to transplant seedlings into these larger pots. Each new pot needs about 27 cubic inches of soil. The amount of soil s (in cubic inches) it takes to fill p pots is given by the function s 5

  37. algebra

    What is cubic polynomial function in standard form with zero 1, -2, and 2

  38. Whats the answer

    Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. 2-11x^2-8x+6x^2. A) -5x^2-8x+2; quadratic trinomial B) -5x^2-8x; quadratic binomial C) -6x^2-8x-2; cubic polynomial D) -8x+2; cubic trinomial

  39. algebra

    A cubic polynomial function f(x) has leading coefficient -2 and intercepts the y-axis at 2. If f(1)=1, and f(-2)=-2, find f(-1) and write the complete function.

  40. Calculus

    The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12

  41. Calculus

    55. Find an equation of the tangent line to the graph of f(x) =x^3 - 2x + 1 a) at (2,5); b) at (-1,2); c) at (0,1). I believe the answers are: a) y= (3/2 x) - (3/2) b) No solution c) No solution For each function, find the points on the graph at which the

  42. Math

    Suppose you have a graph of a polynomial function and you can see that the function increases without bound on both left and right ends, has 4 real zereos and has 5 turning points. Based on this information, what is the minimum degree of the polynomial?

  43. Algebra 2

    Describe the end behavior of the graph of the polynomial function. Then evaluate the function for x=-4, -3, -2, -1, 0, 1, 2, 3, 4. Then graph the function. Number one: y=x^4-2x^2-x-1

  44. cal

    Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. y(x) = 6x/(x-9)^2 when i workout this problem I get this: by quotient rule: dy/dx = ( (x-9)^2 (6) - 6x(2)(x-9))/(x-9)^4 = 0 at a horizontal tangent 6(x-9)^2 -

  45. math

    You are designing a rain gutter made from a piece of sheet metal that is 1 foot by 5 feet. The gutter is formed by turning up two sides. You want the rain gutter to have the greatest volume possible. Below is the polynomial function that represents the

  46. Math

    2-4 paragraphs plus two graphs Details: Many different kinds of data can be modeled using polynomial functions. An example of a polynomial function would be gas mileage for an automobile. If we compare gas mileage at two different speeds, V1 and V2, the

  47. math

    This is a continuous from my last question Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2) with x ≠ 2. On what intervals is the graph of g concave down? Justify your answer.

  48. math, a.p. calc

    Let g be a function that is defined for all x, x ≠ 2, such that g(3)=4 and the derivative of g is g′(x)= x^2–16/x−2, with x≠2. Write an equation for the tangent line to the graph of g at the point where x = 3. Does this tangent line lie above or

  49. Precalculus

    find the equation of the cubic equation show graph passes through the points (3,0) and (1,4) and is tangent to the axis at the origin??? I honestly cannot figure this out and can you explain the graph to me too?

  50. math

    With regards to question J: The variables x and y are connected by the equation y = x2 - x - 5. Some corresponding values of x and y are given in the table below. x -4 -3 -2 -1 0 1 2 3 4 5 y 15 7 a -3 -5 b -3 1 7 15 (a) Calculate the values of a and b (b)

  51. algebra

    find the following for the function f(x)= (x+5)^2(x-1)^2 a) find the x and y intercepts for the polynomial function f b) determine whether the graph of f crosses or touches the x axis at each x intercept C) put all information together to obtain the graph

  52. 8th Grade Algebra

    Multiply. 1) (3t^2 - 2t - 4) * (5t + 9) Writing. 1) Explain why the product of a quadratic polynomial and a linear polynomial must be a cubic polynomial.

  53. Calculus

    consider the function y = 2sinx a) determine dy/dx b) calculate the exact value of x for which the slope of the tangent to the graph is √2 in the interval [0, pie] c) determine the equation of the tangent in part (b). d) determine the y-intercept of the

  54. Math

    Determine whether the following statement makes sense or does not make sense, and explain your reasoning: When I'm trying to determine end behavior, it's the coefficient of the leading term of a polynomial function that I should inspect. A) This makes

  55. calculus

    Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.f(x)= x^2 - 5x +2 (1, -2)

  56. Calculus

    Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = -2x2-2x+1 (-1, -2)

  57. calculus

    Write the equation of the tangent line to the curve at the indicated point. As a check, graph both the function and the tangent line. f(x) = x7 − 7 at x = −1 7 x7

  58. Calculus

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/(4 x) at (1,(15/4) m = y =

  59. Math

    Let f(x) be a cubic polynomial function such that y=13(x-1)+4 is tangent to the graph of f(x)at (1, 4) and y=(x+1)+6 is tangent to the graph of f(x) at (-1, 6). Find the equation of f(x)

  60. Calculus

    A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and the graph of f has a point

  61. Math

    How can I determine a value of gradient from a graph if the line is curved. (not a straight line) This is where Calculus comes in If a graph is a curve, then the gradient (slope) of the curve is the slope of the tangent that you draw at a particular point

  62. MATH TRIGONOMETRY

    refer to the polynomial function f(x)= -x(x-1)(x+2) in anwering the folloowing questions. 1.what is the y intercept? 2.what is the behavior of the left end of its graph? 3.will the graph pass through the origin? 4,what is the behavior of the left end of

  63. cal

    find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8 find the equation of the tangent lines at x=1 and x=-2 graph the quadratic

  64. Graphs of polynomial functions

    What do polynomial functions look like? And what can be consider a polynomial function? Would a graph that is like an upside down V be considered as a graph of a polynomial function?

  65. Polynomial Functions

    What do polynomial functions look like? And what can be consider a polynomial function? Would a graph that is like an upside down V be considered as a graph of a polynomial function?

  66. Polynomial Functions-help

    What do polynomial functions look like? And what can be consider a polynomial function? Would a graph that is like an upside down V be considered as a graph of a polynomial function?

  67. College Math

    2008 (2nd)Course2-4.1 We are to find a function f(x) such that its derivative is x^2+x-1 and the graph of y=f(x) is tangent to the straight line y=x+1. First we find the coordinates of the point at which y=f(x) and y=x+1 are tangent.Since the slope of the

  68. AP CALC. AB

    2. A cubic function is a polynomial of degree 3 and has the form y=mx^3+bx^2+cx+d; m≠0. What is the maximum quantity of local extreme values a given cubic function can have? a. 2 b. 1 c. 0 d. 3 Is it (a)?? 2. Let f(x)=xln(x). The minimum value attained

  69. Calculus

    1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. The point (a, b) is on the graph of f and the line tangent to the graph at (a, b) passes through the point

  70. calculus totally confused

    find a first degree polynomial function p(1) whose value and slope agree with the value and slope of f at x=c. i think you use taylor series for this f(x)=4/sqrt(x), c=1 i'm totally confused on how to do it. i know you find the derivative but how do i get

  71. calculus

    Hello there, assistance would be terrific, thank you very much. Consider the function f(x)= x^3 + 2x^2 + bx. a) The equation of the tangent line to the graph of this function at x = 1 is given by y = ? b) The tangent line intersects the x-axis at x = ? c)

  72. math

    help me ..... Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation of the line normal to the graph of f(x) when x= pie/6 . (b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal. (c)Find the

  73. math

    help me ..... Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation of the line normal to the graph of f(x) when x= pie/6 . (b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal. (c)Find the

  74. math

    Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation of the line normal to the graph of f(x) when x= pie/6 . (b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal. (c)Find the absolute extrema

  75. calculus

    A cubic polynomial function f is defined by f(x)= 4x^3+ab^2+bx+k where a, b, k, are constants. The function f has a local minimum at x=-2 A. Fine the vales of a and b B. If you integrate f(x) dx =32 from o to 1, what is the value of K?

  76. Math

    Okay I have a scatterplot, so I have points on the graph. I need to use these points (without using regression on my TI-83) to discover a cubic function that would fit the data (as a sort of trend line). How do I go about this? I looked up the graphing

  77. Calculus c

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at x=-1 and x=3 and has a

  78. pre calculus

    find the following for the function f(x)=(x+3)^2(x-1)^2 a.) find the x and y intercept of the polynomial function f. b.)find the power function that the graph of f ressembles for large values of lxl. c.)determine the maximum number of turning pointsof the

  79. College Algebra

    1.The graph of y = - 1/2 |x - 5| - 3 can be obtained from the graph of y = |x| by which transformations? What is the horizontal shift? By what factor is the graph stretched or shrunk vertically and how is it reflected? What is the vertical shift? 2. Find

  80. Math

    Hello! I've been having trouble deciding what type of function this equation is: y=√x / x^2+8 There are a couple possbilties to pick from such as; power, root, rational, algebraic, polynomial by degree 2 and polynomial by degree 8. I thought it would be

  81. Algebra 1

    A gardener at a nursery is filling pots with soil to prepare to transplant seedlings into these larger pots. Each new pot needs about 27 cubic inches of soil. The amount of soil s (in cubic inches) it takes to fill p pots is given by the function s 5

  82. maths

    what is the coefficient of (x+2)^3 in the cubic taylor polynomial about -2 for the function f(x)= e^x?

  83. Calculus

    Score for Question 2: ___ of 40 points) For the polynomial (x)=x^5-5x^4+12x^3-24x^2+32x-16 , answer the following questions. Show all of your work. How many zeros does the function have over the set of complex numbers? What is the maximum number of local

  84. Calculus

    Suppose f(x)= e^(-1/x). Graph this function in the window -5(

  85. Calculus

    Suppose f(x)= e^(-1/x). Graph this function in the window -5(

  86. Applied Calculus......

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=6x-5x^2 at (-2, -32) I have to use the four step process, but seem to be getting stuck...

  87. Calculus PLEASE HELP

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 2 x - 4 x^2( at ) (-2,-20) m= y=

  88. Math

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 9/(5 x) ( at ) \(1,(9/5)) m = y=

  89. Calculus

    Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why f(x) must have a root between x=-3 and x=-2 b) Write an equation of the line perpendicular to the graph of f at x=0 c) Find the x and y coordinates of the point on the graph of f where

  90. Calculus

    Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why f(x) must have a root between x=-3 and x=-2 b) Write an equation of the line perpendicular to the graph of f at x=0 c) Find the x and y coordinates of the point on the graph of f where

  91. Calculus grade 12 exam review PLEASE HELP ASAP !!

    PLEASE HELP ME! Exam is in an hour and i need to finish this exam pre-test to help me ! consider the function y = 2sinx a) determine dy/dx b) calculate the exact value of x for which the slope of the tangent to the graph is √2 in the interval [0, pie] c)

  92. Math

    The function f(x) = x^2 -2x + x^1/2 is: A. A polynomial because it is continuous. B. A polynomial because it is of the form axn. C. Not a polynomial because you are subtracting 2x. D. Not a polynomial because you can’t have any fractional exponents. Is

  93. algebra 2

    decribe the end behavior of the graph of the polynomial function.then evaluate the function for x=-4,-3,-2...,4. equation is y=x^4-2x^2-x-1

  94. Algebra

    Find the following function f(x)=(x+3)^2(x-1)^2 (a)Find the x and y intercept of the polynomial function f. (b) Determine whether the graph of the f crosses or touches the x-axis at each x intercept. (c) Put all the information to obtain the graph of f.

  95. algebra 2

    Write a polynomial function that has the zeros 2, -2, and -1 and has a leading coefficient of 1. Then graph the function to show that 2, -2, and -1 are solutions.

  96. AP Calculus

    Let f be a differentiable function with f(-3)= 1 and f'(−3)= 1 and f'(-3)= -5 Let the function g(x)=3[f(x)]^2 Write the equation of the line tangent to the graph of gg at the point where x= -3

  97. Calculas

    The slope of the tangent line to the graph of a function, h(t) is 7/2t The function passes through the point (5,3) Find h(4)

  98. algebra

    Evaluate each of the functions below at x = 1, 2, 4, 8, and 16. Plot the graph of each function. Classify each as linear, quadratic, polynomial, exponential, or logarithmic, and explain the reasons for your classifications. Compare how quickly each

  99. calculus

    is the function f(x)=x^2 increasing on decreasing at x = -1. can anyone please check my reasoning: the value of the derivative of the function at x=-1 is -2, so that means the slope of the tangent line to the graph at that is a negative value so the

  100. Calculus

    Given the function y=(x^2-5/x+3), answer the following questions. a) Find dy/dx. Simplify your answer b) Find the coordinates of any points on the graph of y where the tangent line is horizontal. Show your work. c) Are there any points on the graph of y

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